Abstract
This work presents a data-driven design approach to hierarchical hybrid structures with multiple lattice configurations. Two design variables are considered for each lattice substructure, one discrete variable indicating the configuration type and the other continuous density variable determining the geometrical feature size. For each lattice configuration, a series of similar lattice substructures are sampled by varying the density variable and a corresponding data-driven interpolation model is built for an explicit representation of the constitutive behavior. To reduce the model complexity, substructuring by means of static condensation is performed on the sampled lattice substructures. To achieve hybrid structure with multiple lattice configurations, a multi-material interpolation model is adopted by synthesizing the data-driven interpolation models and the discrete lattice configuration variables. The proposed approach has proved capable of generating hierarchically strongly coupled designs, which therefore allows for direct manufacturing with no post-processing requirement as required for homogenization-based designs due to the assumption on scales separation.
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Funding
This work is supported by the National Natural Science Foundation of China (51705165, 11972166, 51790171, 51975227) and the Fundamental Research Funds for the Central Universities (2019kfyXKJC044).
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MATLAB codes for the cantilever example presented in Figs. 6c and 7c are available as supplementary material. Design cases of the half MBB beam can be easily replicated with the provided codes by changing the boundary conditions.
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Liu, Z., Xia, L., Xia, Q. et al. Data-driven design approach to hierarchical hybrid structures with multiple lattice configurations. Struct Multidisc Optim 61, 2227–2235 (2020). https://doi.org/10.1007/s00158-020-02497-4
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DOI: https://doi.org/10.1007/s00158-020-02497-4